Mathematics & Statistics

• CAS MA 196: Introductory Quantitative Biology
  An introduction to the application of mathematics to problems in biology, with particular emphasis on questions arising from ecology, physiology, neuroscience, and genetics. Major focus on building mathematical models for biological problems and analysis with graphical and mathematical techniques. Also offered as CAS BI 196.
• CAS MA 213: Basic Statistics and Probability
  Students may receive credit for not more than one of the following courses: CAS MA 113, MA 115, or MA 213. Elementary treatment of probability densities, means, variances, correlation, independence, the binomial distribution, the central limit theorem. Stresses understanding and theoretical manipulation of statistical concepts. Carries MCS divisional credit in CAS.
• CAS MA 214: Applied Statistics
  Students may receive credit for not more than one of the following courses: CAS MA 116, MA 214, or MA 614. Inference about proportions, goodness of fit, student's t-distribution, tests for normality; two-sample comparisons, regression and correlation, tests for linearity and outliers, residual analysis, contingency tables, analysis of variance. Carries MCS divisional credit in CAS.
• CAS MA 225: Multivariate Calculus
  Vectors, lines, planes. Multiple integration, cylindrical and spherical coordinates. Partial derivatives, directional derivatives, scalar and vector fields, the gradient, potentials, approximation, multivariate minimization, Stokes's and related threorems. (Cannot be taken for credit in addition to CAS MA 230.)
• CAS MA 226: Differential Equations
  First-order linear and separable equations. Second-order equations and first-order systems. Linear equations and linearization. Numerical and qualitative analysis. Laplace transforms. Applications and modeling of real phenomena throughout. (Cannot be taken for credit in addition to CAS MA 231.)
• CAS MA 230: Honors-Level Vector Calculus
  Linear algebra: linear transformations and matrices, inner products, cross products. Differentiation: tangent spaces, directional derivatives, gradients, vector fields and flow, divergence, curl. Integration: multiple integrals, line integrals, Green's theorem, surface integrals, Stokes's theorem, the divergence theorem. (Cannot be taken for credit in addition to CAS MA 225.)
• CAS MA 231: Honors-Level Differential Equations
  Ordinary differential equations with applications to mechanics, biology, and physics. First- and second-order equations, linear and nonlinear systems, Sturm-Louisville problems, vibrating strings, special functions, power series solutions, regular singular points, Laplace transforms, calculus of variations, isoperimetric problems, and Hamilton's principle. (Cannot be taken for credit in addition to CAS MA 226.)
• CAS MA 242: Linear Algebra
  Matrix algebra, solution of linear systems, determinants, Gaussian elimination, fundamental theory, row-echelon form. Vector spaces, bases, norms. Computer methods. Eigenvalues and eigenvectors, canonical decomposition. Applications. (Cannot be taken for credit in addition to CAS MA 142, MA 442, or ENG EK 102.)
• CAS MA 293: Discrete Mathematics
  Propositional logic, set theory. Elementary probability theory. Number theory. Combinatorics with applications.
• CAS MA 294: Applied Abstract Algebra
  Abstract algebra and its applications to combinatorics. A first exposure to groups, rings, and fields via significant combinatorial applications. Students who have already received credit for MA 541 or MA 542 may not subsequently receive credit for MA 294.
• CAS MA 341: Introduction to Number Theory
  Study of integers and basic results of number theory. Topics include Linear Diophantine equations, prime numbers and factorization, congruences, and quadratic reciprocity.
• CAS MA 381: Elementary Probability
  A calculus-based introductory course in probability. Language of probability, combinatorics, conditional probability, discrete and continuous random variables, the Poisson process, joint probability distribution, moment generating function, law of large numbers and central limit theorem, sample estimators for mean and variance. Cannot be taken for credit in addition to CAS MA 581.
• CAS MA 401: Senior Independent Work
  
• CAS MA 402: Senior Independent Work
  
• CAS MA 411: Advanced Calculus
  Extends concepts and techniques of calculus and develops further applications. Topics include higher dimensional calculus, applications of vector analysis, uniform convergence of series, complex series, improper integrals, gamma and beta functions, Stirling's formula, Fourier series and transform.
• CAS MA 412: Complex Variables
  Basic concepts, results, and applications of complex analysis. Emphasis on computation and applications. Complex plane and functions, differentiability, Cauchy-Riemann conditions, contour integrals, Cauchy formulas, complex series, residue calculus, applications. Extends the concepts of the calculus to the complex setting.
• CAS MA 416: Analysis of Variance
  Fundamental concepts and analytical skills in analysis of variance, including crossed and nested designs, as well as fixed- and random- effect models. Trend analysis for repeated measures, expected mean squares, and non-parametric techniques. SAS is used throughout the course.
• CAS MA 442: Honors Level Linear Algebra
  A thorough development of the fundamentals of linear algebra. Systems of linear equations; matrices, linear transformations, duality; determinants, characteristic and minimal polynomials; diagonalization and normal forms of linear transformations; inner products, unitary and self-adjoint operators, and spectral theory. Applications to physics, probability, and statistics. (Cannot be taken for credit in addition to CAS MA 242.)
• CAS MA 471: Chaotic Dynamical Systems
  Iteration of functions in one and higher dimensions. Periodic points; hyperbolicity; recurrence; topological conjugacy and structural stability; chaotic dynamics. Some numerical experimentation involving personal computers.
• CAS MA 491: Directed Study
  

Back to full list of Courses